TSTP Solution File: GRP421-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP421-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:18:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP421-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 02:19:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --no-flatten-goal
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.41 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))) = Y.
% 0.19/0.41
% 0.19/0.41 Lemma 2: multiply(X, multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W)) = multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W)).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(X, multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))), multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))), multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W))), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), inverse(multiply(inverse(multiply(inverse(W), inverse(multiply(inverse(multiply(Y, Z)), multiply(inverse(inverse(multiply(inverse(W), W))), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(multiply(inverse(W), W))))))))), multiply(inverse(W), inverse(multiply(inverse(W), W))))))), multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W))), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 inverse(multiply(inverse(multiply(U, inverse(multiply(multiply(inverse(W), inverse(multiply(inverse(multiply(Y, Z)), multiply(inverse(inverse(multiply(inverse(W), W))), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(multiply(inverse(W), W)))))))), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(W), inverse(multiply(inverse(multiply(Y, Z)), multiply(inverse(inverse(multiply(inverse(W), W))), inverse(multiply(inverse(inverse(multiply(inverse(W), W))), inverse(multiply(inverse(W), W))))))))), multiply(inverse(W), inverse(multiply(inverse(W), W))))))), multiply(V, W))), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W))), multiply(inverse(T), inverse(multiply(inverse(T), T))))))), multiply(U, T)))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W))
% 0.19/0.41
% 0.19/0.41 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z)) = Y.
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))
% 0.19/0.41 = { by axiom 1 (single_axiom) R->L }
% 0.19/0.41 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.19/0.41 = { by axiom 1 (single_axiom) }
% 0.19/0.41 Y
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(inverse(a1), a1)
% 0.19/0.41 = { by lemma 3 R->L }
% 0.19/0.41 multiply(inverse(a1), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(a1)), multiply(inverse(Y), inverse(multiply(inverse(Y), Y))))))), multiply(X, Y)))
% 0.19/0.41 = { by lemma 2 }
% 0.19/0.41 multiply(inverse(multiply(Z, multiply(X, Y))), multiply(Z, multiply(X, Y)))
% 0.19/0.41 = { by lemma 2 R->L }
% 0.19/0.41 multiply(inverse(b1), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(b1)), multiply(inverse(Y), inverse(multiply(inverse(Y), Y))))))), multiply(X, Y)))
% 0.19/0.41 = { by lemma 3 }
% 0.19/0.41 multiply(inverse(b1), b1)
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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